Towards a Unified Belief Structure in Games with indeterminate probabilities

TL;DR

This paper analyzes and synthesizes various formal belief representations in epistemic game theory with indeterminate probabilities, aiming to unify different belief structures while considering decision-theoretic principles.

Contribution

It introduces conditions that unify different doxastic models in the presence of indeterminate probabilities, addressing the no subjective probability for self-action principle.

Findings

Different belief models can be coherently unified under specific conditions.

Conditions for interrelationships between belief structures are established.

The synthesis respects the decision-theoretic principle of no subjective probability for self-action.

Abstract

This paper provides an analysis of different formal representations of beliefs in epistemic game theory. The aim is to attempt a synthesis of different structures of beliefs in the presence of indeterminate probabilities. Special attention is also paid to the decision-theoretic principle known as the thesis of no subjective probability for self-action. Conditions in cope with this principle are given which underlie the interrelationships between different models of beliefs, and it is shown that under these conditions different doxastic structures can be coherently unified.